The only really simple solution to have several parallel batteries supplying the same load is to replace your fets with diodes. The diodes can be low drop schottky types, but you still easily lose 10% of the voltage. Note: no charging is possible through those diodes.
The zener diodes have no place here until you have some complex active circuit.
In theory you could have a multi-input switching regulator and a controller that that takes the next pulse from the battery that has most charge still left. You need only one set of inductive and output circuitry, but the circuit that distributes the intake load properly to the batteries needs to be developed. There exists battery balancing controller ICs for serial batteries. They're a must in modern high power battery systems. Unfortunately I do not know how they could be adapted for this.